The objective of this grant is to develop statistical methods useful for prevalent cohort data in AIDS studies. The focus will be on two types of prevalent cohorts: (1) prevalent cohort with know time-origins, and (2) prevalent cohort with unknown time-origins. These two types of cohorts share one thing in common, namely, patients in both of the cohorts are recruited according to a certain cross-sectional sampling criterion. However, the data informations differ due to the known and unknown time- origins. The major topics will include non- and semi-parametric methods for one- sample and regression problems. In particular, statistical methods and theory for survival curve estimation, HIV-infection estimation, bootstrapping procedures and proportional hazard model will be developed.